The gross deformations associated with progressive collapse of frame structures lead to the requirement that beam-to-column connections carry significant axial loads in addition to the bending and shears developed under gravity loading. Accurate representations of the relationship between this loading and the corresponding rotations and extensions form an important part of a progressive collapse analysis. The component method of EC3 and EC4 has been developed herein for bare steel and composite connections respectively so as to incorporate the levels of axial load generated by the arching or catenary action seen at various stages of a step-by-step consideration of progressive collapse. Closed form expressions covering the full range of loading and behaviour up to collapse are developed. They have been validated against both the small number of available tests and results obtained from rigorous numerical analyses using ADAPTIC.